Similarly, for the regularization term about \(\mathbf {X}_l^i\)  in problem (REF ), it can be modeled as a zero-mean circularly-symmetric complex Gaussian prior distribution over the columns of the factor matrices as follows [1]}.
\(p\left({\lbrace \mathbf {X}_l^i\rbrace _{l=1}^{L}}_{i=1}^{d}|\lbrace \gamma _k\rbrace _{k=1}^{K}\right)=\prod _{l=1}^{L}\prod _{i=1}^{d}\prod _{k=1}^{K}\mathcal {CN}\left(\mathbf {X}_{l}^i(:,k)|\mathbf {0},\gamma _k^{-1}\mathbf {I}\right).\) 
